Late Thursday at the New Orleans Arena, Alicia Keys accompanied herself on piano for “Not Even the King.” “They can’t afford what we got,” she sang, her voice as precise as her bob haircut, “not even the king.” The ballad, a deep cut from her current “Girl on Fire” CD, came across as a forthright pledge of devotion, based on the premise that material possessions – crowns, castles, diamonds -- are no substitute for love.

Keys would do well to apply that same principle to her stage show. Expressions of emotion, intimacy and/or elation – even quiet ones -- trump bells and whistles every time.

As evidenced by her just jazzy enough take on the national anthem prior to Super Bowl XLVII in the Mercedes-Benz Superdome – and by Thursday’s “Not Even the King” -- she requires little more than her voice and a piano to hold an audience rapt. But because her Set the World on Fire Tour is booked into big arenas, she and her team apparently felt she needed more.

Case in point: The four male interpretative dancers/actors who occasionally materialized, costumed in suits or as New York B-boys and other obvious characters. The absence of any spark whatsoever between Keys and the guy who shimmied against her in “Un-thinkable (I’m Ready)” was glaring. Another fellow’s thankless task was to mime a cell phone conversation with Keys in “You Don’t Know My Name” – a ridiculous, and pointless, gambit. “A Woman’s Worth” was not enhanced by aggressive electric guitars and a flashy, James Bond-ian light and video presentation. More was less.

Thursday’s modest crowd offered empirical evidence that, in New Orleans at least, Keys should stick to smaller venues. The New Orleans Arena’s upper deck was completely empty; scattered seats on the floor and lower bleachers were also unsold.

She first appeared in silhouette, wearing a broad-brimmed hat and a sheer top, transparent except for a black strip across her chest, to strut through “Karma.” That launched a nearly two-hour, representative sampling of her five studio albums.

By and large, her songs benefitted from a live treatment. “Tears Always Win” is a bit stiff in recorded form on “Girl on Fire.” Onstage, it opened up and realized its full potential as a soul-pop vamp, especially as the backing vocalists dug into the chorus while a sing-song church organ percolated. “Never See Me Again” – starkly and smartly arranged for solo piano and voice -- was another early highlight.

The most useful male of the night was Maxwell, who appeared in virtual form, on video screens, to reprise his smoldering falsetto “Fire We Make” duet with Keys. Too bad the show’s opening act, Miguel, an R&B crooner of no small talent, didn’t stick around to serve as a flesh-and-blood fill-in for Maxwell.

Keys may not be a force of nature like Beyonce, or boast Jennifer Hudson’s pipes, or Mary J. Blige’s street cred and survivor’s story, or Sade’s effortless sensuality. But she combines elements of those performers with her own well-written contemporary R&B melodies in a presentation that is uniquely her own.

She does not do dirty, or even sweat. As befitting a former Columbia University music major who, one suspects, very much prefers to be fully in control, she leaves little to chance. Her show is meticulously plotted, perhaps to a fault; her canned banter consisted of standard platitudes about following one’s dreams.

Her consistently poised and professional approach eliminates extremes: You don’t get a sloppy mess, but neither do you get the sort of transformative, spine-tingling surprises that mark the most memorable performances.

She seemed out of her element trying to stir up audience participation during uptempo numbers; she was far more comfortable at the piano. In the night’s oddest logistical transition, she bid an extensive goodbye after wrapping up “New Day.” A scrim descended from the rafters, hiding the stage; “Thank you, New Orleans….Love, Alicia” was spelled out on the screen. The show appeared to be over; a not insignificant number of people headed for the exits.

But the set list dictated that she would return for “Empire State of Mind.” Having donned an evening gown – her only costume change of the night – she belted what has become her signature song, one whose luster has started to fade.

The show’s most telling moment occurred earlier. In the especially intimate “101,” the protagonist, against her better judgment, allows herself to become a serial Lothario’s latest victim. The mood is one of resignation and at least partial regret; Keys played the song, and the part, beautifully.

But instead of teasing out the denouement for the audience to savor, she and her band immediately slammed into an amped-up take on her first hit, “Fallin.” The transition was jarring. Keys went for another big gesture, when a small one should have sufficed.

Keith Spera can be reached at kspera@nola.com or 504.826.3470. Follow him on Twitter at KeithSpera.